高指数马鞍动力学预测校正方案的误差估计

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-20 DOI:10.1016/j.cnsns.2025.108852

Wenhao Li , Haotian Lin , Xiaojie Wang

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引用次数: 0

摘要

高指数鞍区动力学为搜索任意指数鞍区点和构建解景观提供了有效途径。本文提出并分析了一种求解高指数马鞍动力学的预测校正数值方法。证明了离散化方案的误差界相对于时间步长是二阶的，不需要对方向变量的数值解进行正交一化。当步长减小到零时，每一步中方向变量的数值解几乎是标准正交的。数值实验证实了我们的理论结果。

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Error estimates of a predictor-corrector scheme for high-index saddle dynamics

High-index saddle dynamics provide an effective way to search for any-index saddle points and construct the solution landscape. In this paper, we propose and analyze a predictor–corrector numerical method for solving high-index saddle dynamics. Error bounds of the discretization scheme are proved to be of second order with respect to the time step size, which do not require the numerical solutions of the directional variables to be orthonormalized. When the step-size shrinks to zero, the numerical solutions of directional variables in every step are shown to be almost orthonormal. Numerical experiments confirm our theoretical results.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.